New frequency domain methods for stability analysis of linear continuous-time fractional order systems with delays of the retarded type are given. The methods are obtained by generalisation to the class of fractional order systems with delays of the Mikhailov stability criterion and the modified Mikhailov stability criterion known from the theory of natural order systems without and with delays. The study is illustrated by numerical examples of time-delay systems of commensurate and non-commensurate fractional orders.
The paper presents the stability problem of control systems composed of a fractional-order PI controller and a inertial plant of a fractional order with time delay. Simple and efficient computational method for determining stability regions in the controller and plant parameters space is given. Knowledge of these regions permits tuning of the fractional-order PI controller. The method proposed is based on the classical D-partition method.
This paper addresses the nonlinear Cucker–Smale optimal control problem under the interplay of memory effect. The aforementioned effect is included by employing the Caputo fractional derivative in the equation representing the velocity of agents. Sufficient conditions for the existence of solutions to the considered problem are proved and the analysis of some particular problems is illustrated by two numerical examples.
The use of fractional-order calculus for system modeling is a good alternative to well-known classic integer-order methods, primarily due to the precision with which the modeled object may be mapped. In this study, we created integer and fractional discrete models of a real object – a highspeed brushless micro-motor. The accuracy of the models was verified and compared.
The efficient, stable and reliable operation of the blast furnace secures the proper quality of coke, which is one of the basic components of the blast furnace charge. In modern blast-furnace technology, when using substitute fuels, i.e. coal dust, the role of coke is extremely important. For this reason, the demands placed on its quality increase. Domestic coking plants have a limited base of Polish high quality coking coals at their disposal, therefore the full use of their coking properties is extremely important. The grain composition of the coal blend is one of the basic factors affecting the quality of the produced coke. This influence depends on the quantity and quality of coal components that make up the blend. In the conducted research, 21 coking coals, differing significantly in the degree of rank and origin (Polish and overseas coals), it was shown that the separated grain classes differ in properties, both coking properties and the degree of devolatalization during heating. In analyzing the obtained results, it was observed that the grain volume growth occurs essentially in the temperature range between the beginning and the maximum of fluidity. It has been shown that there is a linear correlation between the temperature corresponding to maximum fluidity and the temperature at which the maximum rate of evolution of volatiles enters. The presented phenomena accompany the emergence of coal expansion pressure during the coking process and they are its primary causes. The presented results can be an important guide for preparing the milling of coal for the coking process.
In our recent study we demonstrated that the holding of fresh semen in fractionated seminal plasma (SP1, >40 kDa; SP2, <40 kDa), obtained by gel filtration chromatography, significantly improved the sperm quality characteristics following cryopreservation (Wasilewska-Sakowska et al. 2019). In this study we investigated the effect of post-thaw (PT) supplementation of fractionated SP (SP1 and SP2) on the survival of spermatozoa from boars with good and poor semen freezability, GSF and PSF, respectively. Two-dimensional polyacrylamide gel electrophoresis (2D-PAGE) analysis showed distinct differences in the protein profiles of SP1 and SP2 from boars with GSF or PSF regarding the number of protein spots. Sperm motility characteristics and the motion patterns, assessed using the computer-assisted sperm analysis (CASA) system, were markedly higher in PT semen supplemented with SP1 and SP2 from boars with GSF. Post-thaw supplementation of either SP1 or SP2 from boars with GSF significantly improved mitochondrial function, plasma membrane and acrosome integrity, and viability during storage. The findings of this study have confirmed that the presence of protective protein components in varying abundance in either fractionated SP from boars with good freezability ejaculates significantly improved the sperm survival following PT storage.
The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.
The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.
The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.
Antarctic krill carbohydrate content was followed during 1983—84 Eighth Polish Antarctic Expedition. The Admiralty Bay (King George Island) was th area of study. The following average values of three estimated fractions were obtained: 3.77 +- 1.51%, 0.47 +- 0.34% and 3.30 +- 1.33% for total, TCA-soluble and TCA-insoluble carbohydrates, respectively. Percentage contribution of the estimated fractions to dry weight varied seasonally (1.48—7.41%, 0.15—1.83%, and 1.28—6.28%, respectively). The carbohydrate content showed a clearcut cycle of changes over the calender year, with a minimum in autumn-winter and a maximum in spring-summer.
Changes in the amount of basic nitrogen fractions (total, protein and non-protein nitrogen) were studied in an annual cycle. Significant seasonal changes were noted, minima occurring in Antarctic winter and maxima during spring-summer season. These changes are due mainly to high fluctuations of water content in krill in the annual cycle.
In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.